Problem: What do the following two equations represent? $4x-2y = 5$ $-12x+6y = -15$
Answer: Putting the first equation in $y = mx + b$ form gives: $4x-2y = 5$ $-2y = -4x+5$ $y = 2x - \dfrac{5}{2}$ Putting the second equation in $y = mx + b$ form gives: $-12x+6y = -15$ $6y = 12x-15$ $y = 2x - \dfrac{5}{2}$ The above equations turn into the same equation, so they represent equal lines.